Solid geometry, stereometry - page 34 of 120
Number of problems found: 2399
- Three-quarters of volume
A cylindrical container is three-quarters full with six liters of water. We dip a cube-shaped body into the container, which sinks to the bottom. The length of the edge of the cube is 13 cm. Decide what happens to the sink after the cube is dipped. - Millimeter 6629
The ice cube weighs 24g. Determine the size of its edge to the nearest millimeter. If the ice density is 917kg/m3 - Cylinder container
If the cylinder-shaped container is filled with water to a height of 5 dm, it contains 62.8 hectoliters of water. Calculate the diameter of the bottom of the container. Use the value π = 3.14. - Calculate 38073
1. Calculate the volume of a cube whose edge is 3.6 dm long. 2. Calculate the edge's size if you know its surface S = 2166 mm². - Deformed 5992
Fifty small metal cubes with an edge length of 2 cm were deformed, and we made one large cube from this material. What is its surface? - Completely 4226
The aquarium is shaped like a cube and is partially filled with water. For Peter, a cube with an edge of 8 cm fell into it and completely sank. The water level in the aquarium rose by 1 cm. What is the volume of the whole aquarium? - Hemispherical dome
What is the coverage area of the painting of a hemispherical dome with a diameter of 8 m?
- Identical cubes
From the smallest number of identical cubes whose edge length is expressed by a natural number, can we build a block with dimensions 12dm x 16dm x 20dm? - Tetrahedral prism
The height of a regular tetrahedral prism is three times greater than the length of the base edge. Calculate the length of the base edge if you know that the prism volume is 2187 cm³. - Calculate 20893
The volume of the cylinder is 193 cm³, and the radius of its base is 6.4 cm. Calculate the height and surface of the cylinder to 1 decimal place. - Three cubes
Two cube-shaped boxes with edges a = 70 cm; b = 90 cm must be replaced by one cube-shaped box. What will be its edge? - Eight
Eight small Christmas balls with a radius of 1 cm have the same volume as one large Christmas ball. What has a bigger surface: eight small balls or one big ball? - Iron sphere
Iron sphere weights 100 kg and density ρ = 7600 kg/m³. Calculate the volume, surface, and diameter of the sphere. - Prism X
The prism with the edges of the lengths x cm, 2x cm, and 3x cm has a volume 29478 cm³. What is the area of the surface of the prism? - Assembling 63964
Little Pavel was assembling building blocks (a cube is shaped like a cube). He wanted to build a big cube. However, he had 75 dice left, so he increased the edge by one die. Then he was missing 16 dice. How many cubes did he have in the kit?
- Diameter 48211
What is the diameter of the ball (for men) if it weighs 7,250 g and ρ = 7.8g / cm³ - Volumes 7252
The block and the cube have the same volumes of 512 cm3, and the block has edge lengths of b = 6.4 cm and c = 10 cm. Can a cube and a block have the same edge length? - Cube containers
Replace the two cube-shaped containers with 0.8 dm and 0.6 dm edges with a single cube-shaped one to have the same volume as the original ones. What is the length of the edge of this cube? - Cuboid edges in ratio
Cuboid edge lengths are in ratio 2:4:6. Calculate their lengths if you know that the cuboid volume is 24576 cm³. - Cube 5
The surface of the cube is 15.36 dm². How will this cube's surface area change if the edges' length is reduced by 2 cm?
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